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Differentiation

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Question 500

A curve CCC has equation

y=2x3−15x+kx,x>0 y = 2x^3 - 15x + \frac{k}{x}, \quad x > 0 y=2x3−15x+xk​,x>0

where kkk is a constant. The point PPP with xxx-coordinate 111 lies on CCC. Given that PPP is a stationary point of CCC:

a.

show that k=−9k = -9k=−9.

[3]
b.

Determine the nature of the stationary point at PPP, justifying your answer.

[3]
c.

The curve CCC has a second stationary point.

Using algebra, find the xxx-coordinate of this second stationary point.

[4]
Markscheme

Differentiation Questions

  1. A Level
  2. /Maths
  3. /Differentiation

717 exam-style questions on Edexcel A Level Maths Differentiation, covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change. Each one has a worked solution and a mark scheme showing where the marks go.

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